Jermaine Beckford, who was called into the second-string line-up at short notice, created the opening for Howson after his run and shot forced Matthew Upson to scramble the ball off the line.
Howson was perfectly placed to collect the rebound and beat City goalkeeper Colin Doyle with a low finish.
Beckford was a constant threat, hitting the side netting and forcing Doyle into an another block, while winger Seb Carole saw his shot saved at the near post.
City had their chances too as Neil Sullivan produced an excellent save to keep out a lob from Nick Wright.
Peter Till also had the opportunity to snatch an equaliser but drove his shot past the post.
Beckford, Sullivan and Carole were three of four senior players involved, and Paul Butler completed 90 minutes in the centre of Geddis' defence.
Leeds: Sullivan, Madden (Wilkinson 35), Camfield, Hird, Butler, Bayly, Gardner (Rothery 79), Rose, Beckford, Howson, Carole.
Subs Unused: Lund, Ameobi, Brown.